Essays in Group Theory

  • S. M. Gersten

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 8)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Gilbert Baumslag, Peter B. Shalen
    Pages 1-14
  3. M. Gromov
    Pages 75-263
  4. Peter B. Shalen
    Pages 265-319
  5. John R. Stallings
    Pages 321-342

About this book

Introduction

Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings' explicit construction of free actions of orientable surface groups on R-trees. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen's article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers.

Keywords

Group theory algebra group action representation theory

Editors and affiliations

  • S. M. Gersten
    • 1
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9586-7
  • Copyright Information Springer-Verlag New York 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9588-1
  • Online ISBN 978-1-4613-9586-7
  • Series Print ISSN 0940-4740
  • About this book